Skip to main content
SpringerLink
Log in

Self-converse large sets of pure hybrid triple systems

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

A hybrid triple system of order v, briefly by HTS (v), is a pair (X, B) where X is a v-set and B is a collection of cyclic and transitive triples (called blocks) on X such that every ordered pair of X belongs to exactly one block of B. An HTS (v) is called pure and denoted by PHTS (v) if one element of the block set {(x, y, z), (z, y, x), (z, x, y), (y, x, z), (y, z, x), (x, z, y), 〈x, y, z〉, 〈z, y, x〉} is contained in B then the others will not be contained in B. A self-converse large set of disjoint PHTS (v)s, denoted by LPHTS*(v), is a collection of 4(v − 2) disjoint PHTS (v)s which contains exactly (v − 2)/2 converse octads of PHTS (v)s. In this paper, some results about the existence for LPHTS*(v) are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fan, B., Zhou, J. Large sets of pure directed triple systems with index ?. Acta Math. Sin. (Engl. Ser.), 26: 1899–1914 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ji, L. Existence of Steiner quadruple systems with a spanning block design. Discrete Math., 312: 920–932 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kang, Q., Lei, J. On large sets of hybrid triple systems. J. Statist. Plann. Inference, 51: 181–188 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lei, J., Fan, C., Zhou, J. Self-converse large sets of pure Mendelsohn triple systems. Acta Math. Sin. (Engl. Ser.), 25: 1665–1680 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lindner, C. Construction of large sets of pairwise disjoint transitive triple systems II. Discrete Math., 65: 65–74 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  6. Teirlinck, L. Large sets with holes. J. Combin. Des., 1: 69–94 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  7. Tian, Z. On large sets and overlarge sets of combinatorial designs. Dissertation for the Doctoral Degree. Hebei Normal University, Shijiazhuang, 2003 (in Chinese)

    Google Scholar 

  8. Zhou, J., Chang, Y., Ji, L. The spctrum for large sets of pure directed triple systems. Sci. China Ser. A, 36: 764–788 (2006)

    Google Scholar 

  9. Zhou, J., Chang, Y., Ji, L. The spectrum for large sets of pure Mendelsohn triple systems. Discrete Math., 308: 1850–1863 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Bing-li Fan

Authors
  1. Bing-li Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bing-li Fan.

Additional information

Supported by Tianyuan Mathematics Foundation of National Natural Science Foundation of China (No. 11126285).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, Bl. Self-converse large sets of pure hybrid triple systems. Acta Math. Appl. Sin. Engl. Ser. 33, 515–528 (2017). https://doi.org/10.1007/s10255-017-0680-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-017-0680-3

Keywords

2000 MR Subject Classification

Search

Navigation